Experimental and numerical study of noise effects in a FitzHugh–Nagumo system driven by a biharmonic signal

Bordet, Maxime; Morfu, Savério

doi:10.1016/j.chaos.2013.05.020

Cited by 28 publications

(11 citation statements)

References 56 publications

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“…As the correlation time τ increases, it is seen in figure 4 that the minimum MSE value at the optimal σ η increases. The characteristic behaviour for stochastic resonance is in good agreement with results in [ 5 , 19 , 30 – 32 ]. The reason is that, since the variance

of the OU noise is D / τ in equation ( 3.3 ), the noise strength D increases proportionally with the increase of τ for a given

.…”

Section: Resultssupporting

confidence: 88%

“…Beyond the memoryless nonlinearity considered in figure 1 , we argue that this Kalman–LMS adaptive algorithm may potentially be extended to other nonlinear systems, for instance, the Hodgkin–Huxley neuron model [ 5 ], the reduced FitzHugh–Nagumo neuron model [ 4 , 32 , 34 ], the auditory model [ 6 , 7 , 16 ] or biomedical devices [ 38 ]. However, the dynamical nonlinear system has its intrinsic time scale that controls the evolution of the system state.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

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Adaptive recursive algorithm for optimal weighted suprathreshold stochastic resonance

Duan

Gao

et al. 2017

R. Soc. open sci.

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Suprathreshold stochastic resonance (SSR) is a distinct form of stochastic resonance, which occurs in multilevel parallel threshold arrays with no requirements on signal strength. In the generic SSR model, an optimal weighted decoding scheme shows its superiority in minimizing the mean square error (MSE). In this study, we extend the proposed optimal weighted decoding scheme to more general input characteristics by combining a Kalman filter and a least mean square (LMS) recursive algorithm, wherein the weighted coefficients can be adaptively adjusted so as to minimize the MSE without complete knowledge of input statistics. We demonstrate that the optimal weighted decoding scheme based on the Kalman–LMS recursive algorithm is able to robustly decode the outputs from the system in which SSR is observed, even for complex situations where the signal and noise vary over time.

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of the OU noise is D / τ in equation ( 3.3 ), the noise strength D increases proportionally with the increase of τ for a given

.…”

Section: Resultssupporting

confidence: 88%

Section: Conclusion and Discussionmentioning

confidence: 99%

Adaptive recursive algorithm for optimal weighted suprathreshold stochastic resonance

Duan

Gao

et al. 2017

R. Soc. open sci.

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“…On the other hand, the analytical integrability of the FitzHugh–Nagumo system depending on the parameters

a, b, c, d \in double-struckR

has been studied in , and noise perturbation of this differential system were considered in .…”

Section: Introduction and Statements Of The Main Resultsmentioning

confidence: 99%

Zero‐Hopf bifurcation in the FitzHugh–Nagumo system

Euzébio

Llibre

Vidal

2014

Math Methods in App Sciences

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Communicated by A. MiranvilleWe characterize the values of the parameters for which a zero-Hopf equilibrium point takes place at the singular points, namely, O (the origin), P C , and P in the FitzHugh-Nagumo system. We find two two-parameter families of the FitzHugh-Nagumo system for which the equilibrium point at the origin is a zero-Hopf equilibrium. For these two families, we prove the existence of a periodic orbit bifurcating from the zero-Hopf equilibrium point O. We prove that there exist three two-parameter families of the FitzHugh-Nagumo system for which the equilibrium point at P C and at P is a zero-Hopf equilibrium point. For one of these families, we prove the existence of one, two, or three periodic orbits starting at P C and P .

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“…In fact, for an optimal value of the perturbation, the system enhances its response to the low-frequency excitation. Therefore, the detection of the low frequency by the nonlinear system is enhanced by the HF perturbation [16–18]. Similar to the SR effect, it is then not surprising that VR has been proved to occur in neurons models [19] and in neural networks [20,21], leading to applications in one-dimensional signal processing.…”

Section: Introductionmentioning

confidence: 99%

On some applications of vibrational resonance on noisy image perception: the role of the perturbation parameters

Morfu¹,

Usama²,

Marquié³

2021

Phil. Trans. R. Soc. A.

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In this paper, we first propose a brief overview of nonlinear resonance applications in the context of image processing. Next, we introduce a threshold detector based on these resonance properties to investigate the perception of subthreshold noisy images. By considering a random perturbation, we revisit the well-known stochastic resonance (SR) detector whose best performances are achieved when the noise intensity is tuned to an optimal value. We then introduce a vibrational resonance detector by replacing the noisy perturbation with a spatial high-frequency signal. To enhance the image perception through this detector, it is shown that the noise level of the input images must be lower than the optimal noise value of the SR-based detector. Under these conditions, considering the same noise level for both detectors, we establish that the vibrational resonance (VR)-based detector significantly outperforms the SR-based detector in terms of image perception. Moreover, we show that whatever the perturbation amplitude, the best perception through the VR detector is ensured when the perturbation frequency exceeds the image size. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

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Experimental and numerical study of noise effects in a FitzHugh–Nagumo system driven by a biharmonic signal

Cited by 28 publications

References 56 publications

Adaptive recursive algorithm for optimal weighted suprathreshold stochastic resonance

Adaptive recursive algorithm for optimal weighted suprathreshold stochastic resonance

Zero‐Hopf bifurcation in the FitzHugh–Nagumo system

On some applications of vibrational resonance on noisy image perception: the role of the perturbation parameters

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